Is Spivak not enough of a cookbook?

[AlwaysCurious]

Hey there,

I'm a high school student learning some basic linear algebra and multivariable calculus. I just ordered Spivak's Calculus on Manifolds, since the book that I've been going through was not as interesting (not a horrible cookbook, but most of the problems could be done without a lot of thought), and since I learned calculus out of his much less terse Calculus, which by and large I really enjoyed (although I did struggle with it quite a bit at the outset).

My question is, will Spivak give me all of the necessary information that one would typically get out of a standard cookbook calc 3 course? It certainly would give me more of an education, but would I learn all of the standard topics covered?

Thank you!
Brian

 

[bcrowell]

The term "calc 3" doesn't have any widely accepted definition.

 

[WannabeNewton]

Spivak is meant to follow up on rigorous single variable calculus proof based course as it goes straight into epsilon delta proofs in multiple dimensions, inverse function theorem, differential forms / exterior calculus, integration on manifolds, stokes theorem etc. Much of this material will not be covered in a typical non honors calculus 3 class in college and much of the standard non honors calc 3 material will not be covered in this book at all. You definitely, definitely, need to have done proof based linear algebra beforehand. He will assume you know what dual spaces are, what bilinear forms are (if I recall correctly), but things like multi - linear forms and tensor products he introduces in the book itself.